wcmdscale {vegan} | R Documentation |
Weighted classical multidimensional scaling, also known as weighted principal coordinates analysis.
wcmdscale(d, k, eig = FALSE, add = FALSE, x.ret = FALSE, w)
d |
a distance structure such as that returned by dist
or a full symmetric matrix containing the dissimilarities. |
k |
the dimension of the space which the data are to be represented in; must be in {1,2,...,n-1}. If missing, all dimensions with above zero eigenvalue. |
eig |
indicates whether eigenvalues should be returned. |
add |
logical indicating if an additive constant c* should be computed, and added to the non-diagonal dissimilarities such that all n-1 eigenvalues are non-negative. Not implemented. |
x.ret |
indicates whether the doubly centred symmetric distance matrix should be returned. |
w |
Weights of points. |
Function wcmdscale
is based on function
cmdscale
(package stats of base R), but it uses
point weights. Points with high weights will have a stronger
influence on the result than those with low weights. Setting equal
weights w = 1
will give ordinary multidimensional scaling.
If eig = FALSE
and x.ret = FALSE
(default), a matrix
with k
columns whose rows give the coordinates of the points
chosen to represent the dissimilarities.
Otherwise, an object of class wcmdscale
list containing the
following components.
points |
a matrix with k columns whose rows give the
coordinates of the points chosen to represent the dissimilarities. |
eig |
the n-1 eigenvalues computed during the scaling process if
eig is true. |
x |
the doubly centred and weighted distance matrix if x.ret is true. |
weights |
Weights. |
Gower, J. C. (1966) Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53, 325–328.
Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Chapter 14 of Multivariate Analysis, London: Academic Press.
cmdscale
.
Also isoMDS
and sammon
in package MASS.
## Correspondence analysis as a weighted principal coordinates ## analysis of Euclidean distances of Chi-square transformed data data(dune) rs <- rowSums(dune)/sum(dune) d <- dist(decostand(dune, "chi")) ord <- wcmdscale(d, w = rs, eig = TRUE) ## Ordinary CA ca <- cca(dune) ## Eigevalues are numerically similar ca$CA$eig - ord$eig ## Configurations are similar when site scores are scaled by ## eigenvalues in CA procrustes(ord, ca, choices=1:19, scaling = 1) plot(procrustes(ord, ca, choices=1:2, scaling=1))